(CNN) — When schools in Kentucky closed for several days last month due to severe flooding, students suddenly began showing up at the Bullitt County Public Library.They had come for the internet.To pay for those high-speed connections that some students lacked at home, the county library – like many others across the country – has relied on a federal program that is now poised for a major overhaul courtesy of the Supreme Court.

“Internet access is a luxury,” said Tara O’Hagan, the library’s executive director. “In Bullitt County, there’s literally a digital divide.”The case, which the justices will hear on Wednesday, could wind up costing libraries, schools and hospitals billions.

At a time when nearly 10% of US households do not have access to broadband internet, one of the leading programs to bridge the divide has been caught up in a broader and decades old separation-of-powers fight over federal agencies. Those cases have found purchase on the 6-3 conservative Supreme Court, which has repeatedly limited the ability of the federal bureaucracy to act absent congressional approval.A conservative “consumer awareness group” is challenging the $7 billion Universal Service Fund, which Congress created in 1996 to offset the cost of phone and internet service for low-income Americans.

It’s a system that critics say is a “bureaucrat’s dream” and a “nightmare for the Constitution.”To pay for programs like E-Rate, which O’Hagan’s library relies on,.